e_rem_pio2f.c revision 152535 
1/* e_rem_pio2f.c -- float version of e_rem_pio2.c
2 * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
3 * Debugged and optimized by Bruce D. Evans.
4 */
5
6/*
7 * ====================================================
8 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
9 *
10 * Developed at SunPro, a Sun Microsystems, Inc. business.
11 * Permission to use, copy, modify, and distribute this
12 * software is freely granted, provided that this notice
13 * is preserved.
14 * ====================================================
15 */
16
17#ifndef lint
18static char rcsid[] = "$FreeBSD: head/lib/msun/src/e_rem_pio2f.c 152535 2005-11-17 02:20:04Z bde $";
19#endif
20
21/* __ieee754_rem_pio2f(x,y)
22 *
23 * return the remainder of x rem pi/2 in y[0]+y[1]
24 * use double precision internally
25 * use __kernel_rem_pio2() for large x
26 */
27
28#include "math.h"
29#include "math_private.h"
30
31/*
32 * Table of constants for 2/pi, 396 Hex digits (476 decimal) of 2/pi
33 */
34static const int32_t two_over_pi[] = {
350xA2F983, 0x6E4E44, 0x1529FC, 0x2757D1, 0xF534DD, 0xC0DB62,
360x95993C, 0x439041, 0xFE5163, 0xABDEBB, 0xC561B7, 0x246E3A,
370x424DD2, 0xE00649, 0x2EEA09, 0xD1921C, 0xFE1DEB, 0x1CB129,
380xA73EE8, 0x8235F5, 0x2EBB44, 0x84E99C, 0x7026B4, 0x5F7E41,
390x3991D6, 0x398353, 0x39F49C, 0x845F8B, 0xBDF928, 0x3B1FF8,
400x97FFDE, 0x05980F, 0xEF2F11, 0x8B5A0A, 0x6D1F6D, 0x367ECF,
410x27CB09, 0xB74F46, 0x3F669E, 0x5FEA2D, 0x7527BA, 0xC7EBE5,
420xF17B3D, 0x0739F7, 0x8A5292, 0xEA6BFB, 0x5FB11F, 0x8D5D08,
430x560330, 0x46FC7B, 0x6BABF0, 0xCFBC20, 0x9AF436, 0x1DA9E3,
440x91615E, 0xE61B08, 0x659985, 0x5F14A0, 0x68408D, 0xFFD880,
450x4D7327, 0x310606, 0x1556CA, 0x73A8C9, 0x60E27B, 0xC08C6B,
46};
47
48/*
49 * invpio2:  53 bits of 2/pi
50 * e1pio2:   1*pi/2 rounded to 53 bits
51 * e2pio2:   2*pi/2 rounded to 53 bits
52 * e3pio2:   3*pi/2 rounded to 53 bits
53 * e4pio2:   4*pi/2 rounded to 53 bits
54 * pio2_1:   first  33 bit of pi/2
55 * pio2_1t:  pi/2 - pio2_1
56 */
57
58static const double
59zero =  0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */
60half =  5.00000000000000000000e-01, /* 0x3FE00000, 0x00000000 */
61two24 =  1.67772160000000000000e+07, /* 0x41700000, 0x00000000 */
62invpio2 =  6.36619772367581382433e-01, /* 0x3FE45F30, 0x6DC9C883 */
63e1pio2  =  1*M_PI_2,                   /* 0x3FF921FB, 0x54442D18 */
64e2pio2  =  2*M_PI_2,                   /* 0x400921FB, 0x54442D18 */
65e3pio2  =  3*M_PI_2,                   /* 0x4012D97C, 0x7F3321D2 */
66e4pio2  =  4*M_PI_2,                   /* 0x401921FB, 0x54442D18 */
67pio2_1  =  1.57079632673412561417e+00, /* 0x3FF921FB, 0x54400000 */
68pio2_1t =  6.07710050650619224932e-11; /* 0x3DD0B461, 0x1A626331 */
69
70	int32_t __ieee754_rem_pio2f(float x, float *y)
71{
72	double z,w,t,r,fn;
73	double tx[3];
74	int32_t e0,i,nx,n,ix,hx;
75
76	GET_FLOAT_WORD(hx,x);
77	ix = hx&0x7fffffff;
78	if(ix<=0x3f490fda)   		/* |x| ~<= pi/4, reduction is null */
79	    {y[0] = x; y[1] = 0; return 0;}
80    /* 53 bit pi is good enough for special cases */
81	if(ix<=0x407b53d1) {		/* |x| ~<= 5*pi/4 */
82	    if(ix<=0x4016cbe3) {	/* |x| ~<= 3*pi/4 */
83		if(hx>0) {
84		    z = x - e1pio2;
85		    n = 1;
86		} else {
87		    z = x + e1pio2;
88		    n = 3;
89		}
90		y[0] = z;
91		y[1] = z - y[0];
92		return n;
93	    } else {
94		if(hx>0)
95		    z = x - e2pio2;
96		else
97		    z = x + e2pio2;
98		y[0] = z;
99		y[1] = z - y[0];
100		return 2;
101	    }
102	}
103	if(ix<=0x40e231d5) {		/* |x| ~<= 9*pi/4*/
104	    if(ix<=0x40afeddf) {	/* |x| ~<= 7*pi/4 */
105		if(hx>0) {
106		    z = x - e3pio2;
107		    n = 3;
108		} else {
109		    z = x + e3pio2;
110		    n = 1;
111		}
112		y[0] = z;
113		y[1] = z - y[0];
114		return n;
115	    } else {
116		if(hx>0)
117		    z = x - e4pio2;
118		else
119		    z = x + e4pio2;
120		y[0] = z;
121		y[1] = z - y[0];
122		return 0;
123	    }
124	}
125    /* 33+53 bit pi is good enough for medium size */
126	if(ix<=0x49490f80) {		/* |x| ~<= 2^19*(pi/2), medium size */
127	    t  = fabsf(x);
128	    n  = (int32_t) (t*invpio2+half);
129	    fn = (double)n;
130	    r  = t-fn*pio2_1;
131	    w  = fn*pio2_1t;
132	    y[0] = r-w;
133	    y[1] = (r-y[0])-w;
134	    if(hx<0) 	{y[0] = -y[0]; y[1] = -y[1]; return -n;}
135	    else	 return n;
136	}
137    /*
138     * all other (large) arguments
139     */
140	if(ix>=0x7f800000) {		/* x is inf or NaN */
141	    y[0]=y[1]=x-x; return 0;
142	}
143    /* set z = scalbn(|x|,ilogb(x)-23) */
144	z = x;
145	GET_HIGH_WORD(hx,z);
146	ix = hx&0x7fffffff;
147	e0 	= (ix>>20)-1046;	/* e0 = ilogb(z)-23; */
148	SET_HIGH_WORD(z, ix - ((int32_t)(e0<<20)));
149	for(i=0;i<2;i++) {
150		tx[i] = (double)((int32_t)(z));
151		z     = (z-tx[i])*two24;
152	}
153	tx[2] = z;
154	nx = 3;
155	while(tx[nx-1]==zero) nx--;	/* skip zero term */
156	n  =  __kernel_rem_pio2(tx,&z,e0,nx,1,two_over_pi);
157	y[0] = z;
158	y[1] = z - y[0];
159	if(hx<0) {y[0] = -y[0]; y[1] = -y[1]; return -n;}
160	return n;
161}
162